Evaluations of annular Khovanov--Rozansky homology

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Gorsky, Eugene, Wedrich, Paul
Format: Preprint
Published: 2019
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914640395501568
author Gorsky, Eugene
Wedrich, Paul
author_facet Gorsky, Eugene
Wedrich, Paul
contents We describe the universal target of annular Khovanov-Rozansky link homology functors as the homotopy category of a free symmetric monoidal category generated by one object and one endomorphism. This categorifies the ring of symmetric functions and admits categorical analogues of plethystic transformations, which we use to characterize the annular invariants of Coxeter braids. Further, we prove the existence of symmetric group actions on the Khovanov-Rozansky invariants of cabled tangles and we introduce spectral sequences that aid in computing the homologies of generalized Hopf links. Finally, we conjecture a characterization of the horizontal traces of Rouquier complexes of Coxeter braids in other types.
format Preprint
id arxiv_https___arxiv_org_abs_1904_04481
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle Evaluations of annular Khovanov--Rozansky homology
Gorsky, Eugene
Wedrich, Paul
Geometric Topology
Representation Theory
We describe the universal target of annular Khovanov-Rozansky link homology functors as the homotopy category of a free symmetric monoidal category generated by one object and one endomorphism. This categorifies the ring of symmetric functions and admits categorical analogues of plethystic transformations, which we use to characterize the annular invariants of Coxeter braids. Further, we prove the existence of symmetric group actions on the Khovanov-Rozansky invariants of cabled tangles and we introduce spectral sequences that aid in computing the homologies of generalized Hopf links. Finally, we conjecture a characterization of the horizontal traces of Rouquier complexes of Coxeter braids in other types.
title Evaluations of annular Khovanov--Rozansky homology
topic Geometric Topology
Representation Theory
url https://arxiv.org/abs/1904.04481